Exploiting multiple antennas for spectrum sensing in cognitive radio networks

ABSTRACT

Spectrum sensing in wireless communications is provided to identify utilized and/or unutilized frequency bands reserved for primary users using a cyclostationary beamforming approach. An adaptive cross self-coherent restoral (ACS) algorithm can be utilized to extract signals of interest (SOI) at unique cycle frequencies related to primary and/or secondary users from an antenna array measurement. Based on the SOI, one or more users of the spectrum can be identified or the spectrum can be regarded as vacant; this can be based on lobe identification in the frequency spectrum of the SOI, in one example. This mechanism is less complex than traditional cyclic spectrum analysis methods. The cyclostationary beamforming based approach is more effective than the energy detection method. Also, the need for quiet periods in spectrum sensing is eliminated when using this mechanism such that signals can be transmitted simultaneously with receiving signals over the antenna array.

TECHNICAL FIELD

The present disclosure relates generally to wireless communicationssystems, and more particularly to spectrum sensing for cognitive radionetworks.

BACKGROUND

Frequency bands for wireless communications are divided among primaryusers (PU), which are licensed to use a certain spectrum for a givenpurpose. For example, cellular networks are allocated a portion of afrequency band for wirelessly transmitting and receiving communicationsignals, as are frequency modulation (FM) radio stations, televisionstations, amateur radio, and/or the like. Such partitioning ensuresdifferent types of signals can be simultaneously communicated withoutsubstantial interference from other sources. The signals can betransmitted in an effort to provide beneficial communication services toone or more users. In many cases, the technologies are allocated largeportions of frequency bands. Due to technological limitations (such assignal power), device location, usage patterns, required bandwidth,etc., portions of given frequency bands may be inefficiently utilizedand/or wasted. For example, in rural areas, much of frequency bandsreserved for FM radio stations can go unutilized as transmitters aremore sparsely deployed as compared to urban areas.

In this regard, cognitive radio (CR) technology has evolved, whichenables wireless communications over unused portions of the frequencybands. Because use of reserved frequency bands can vary over time, CRspossess a cognitive capability to determine frequencies that areunutilized, as well as an ability to reconfigure parameters tocommunicate over the unutilized frequencies. The cognitive capabilitycycle can include spectrum sensing (e.g., radio signal analysis, channelidentification, etc.), cognition/management (e.g., dynamic spectrummanagement, routing, quality-of-service provisioning, etc.), and controlaction (e.g., transmit-power control, adaptive modulation and coding,rate control, etc.).

Spectrum sensing is used to detect presence of a PU related to afrequency band; if the PU is sufficiently sensed, then the CR might notutilize the related spectrum. Sensing can be performed based on energydetection, which facilitates determining whether the frequency band isutilized; however, energy detection does not allow identification of auser occupying the frequency band. Sensing can also be performed usingmatched filtering; however, this requires prior knowledge of detailsrelated to the system for which the spectrum is reserved as well assynchronization thereto, which can be complex. Sensing can also beperformed using feature detection where standards specifics of therelated technology can be identified in a signal to determine whetherthe signal relates to the PU technology. Feature detection, however, ishighly complex to implement and operate.

SUMMARY

The following presents a simplified summary of the claimed subjectmatter in order to provide a basic understanding of some aspects of theclaimed subject matter. This summary is not an extensive overview of theclaimed subject matter. It is intended to neither identify key orcritical elements of the claimed subject matter nor delineate the scopeof the claimed subject matter. Its sole purpose is to present someconcepts of the claimed subject matter in a simplified form as a preludeto the more detailed description that is presented later.

Spectrum sensing techniques that utilize cyclostationary beamforming todetermine a signal of interest (SOI) from an antenna array measurementare provided. This can be accomplished by utilizing adaptive crossself-coherent restoral (ACS), in one example. Based on analyzing theSOI, it can be determined whether a related communication channel isoccupied by a primary user (PU), secondary user (SU), or vacant. Whenoccupied by a PU, the channel can be deemed unavailable forcommunication, whereas if the channel is occupied by a SU or is vacant,it can be utilized for communication, in one example. In addition, forexample, the antenna array can be measured while simultaneouslytransmitting signals over one or more frequencies so long as thetransmitted signals have a different cycle (or conjugate cycle)frequency. Moreover, the spectrum sensing techniques described hereincan be utilized in cognitive radios (CR) communicating over a wirelessnetwork to determine one or more spectrums over which communication isallowed.

To the accomplishment of the foregoing and related ends, certainillustrative aspects of the claimed subject matter are described hereinin connection with the following description and the annexed drawings.These aspects are indicative, however, of but a few of the various waysin which the principles of the claimed subject matter can be employed.The claimed subject matter is intended to include all such aspects andtheir equivalents. Other advantages and novel features of the claimedsubject matter can become apparent from the following detaileddescription when considered in conjunction with the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a high-level block diagram of an example system thatcan spectrum sense in a wireless communication environment.

FIG. 2 illustrates a block diagram of an example cognitive radioemploying spectrum sensing as described herein.

FIG. 3 illustrates a block diagram of an example system for spectrumsensing presence of a primary and/or secondary user.

FIG. 4 illustrates a block diagram of an example system that facilitatescooperative spectrum sensing.

FIG. 5 illustrates an exemplary flow chart for selecting communicationfrequencies based on spectrum sensing.

FIGS. 6-15 illustrate exemplary graphs related to performance ofspectrum sensing mechanisms described herein.

FIG. 16 illustrates a block diagram of an example operating environmentin which various aspects described herein can function.

FIG. 17 illustrates an example wireless communication network in whichvarious aspects described herein can be utilized.

FIG. 18 illustrates an overview of a wireless network environmentsuitable for service by various aspects described herein.

DETAILED DESCRIPTION

The claimed subject matter is now described with reference to thedrawings, wherein like reference numerals are used to refer to likeelements throughout. In the following description, for purposes ofexplanation, numerous specific details are set forth in order to providea thorough understanding of the claimed subject matter. It may beevident, however, that the claimed subject matter may be practicedwithout these specific details. In other instances, well-knownstructures and devices are shown in block diagram form in order tofacilitate describing the claimed subject matter.

As used in this application, the terms “component,” “system,” and thelike are intended to refer to a computer-related entity, eitherhardware, a combination of hardware and software, software, or softwarein execution. For example, a component may be, but is not limited tobeing, a process running on a processor, a processor, an object, anexecutable, a thread of execution, a program, and/or a computer. By wayof illustration, both an application running on a server and the servercan be a component. One or more components may reside within a processand/or thread of execution and a component may be localized on onecomputer and/or distributed between two or more computers. Also, themethods and apparatus of the claimed subject matter, or certain aspectsor portions thereof, may take the form of program code (i.e.,instructions) embodied in tangible media, such as floppy diskettes,CD-ROMs, hard drives, or any other machine-readable storage medium,wherein, when the program code is loaded into and executed by a machine,such as a computer, the machine becomes an apparatus for practicing theclaimed subject matter. The components may communicate via local and/orremote processes such as in accordance with a signal having one or moredata packets (e.g., data from one component interacting with anothercomponent in a local system, distributed system, and/or across a networksuch as the Internet with other systems via the signal).

Additionally, while aspects of the present disclosure are generallydescribed in relation to cognitive radio (CR) communication, it is to beappreciated that the subject matter described herein can be utilized insubstantially any environment for detecting utilized or unutilizedfrequency bands in wireless communications.

Referring to FIG. 1, a high-level block diagram of an example wirelesscommunication system 100 in accordance with various aspects presentedherein is illustrated. The wireless communication system includes aplurality of communicating primary user (PU) components 102-106. Forexample, the PU components 102-106 can utilize a portion of a frequencyband to communicate. The portion of the frequency band can be definedherein as substantially any number of frequency band resources over timeand/or divisions thereof, such as channels, resource blocks, resources,orthogonal frequency division multiplexing (OFDM) symbols, tiles, tones,subcarriers, and/or the like. In addition, the terms are usedinterchangeably herein such that, for example, channels can refer tosubstantially any defined collection of frequency band portions over acollection of time periods. Such collections or portions can be definedin a communication specification for PUs and/or SUs, and/or the like. Inone example, the PU components 102-106 can be configured in a broadcastmode, request/receive, peer-to-peer, and/or the like. Thus, forinstance, PU component 102 can be an access point or broadcast tower,etc., and PU components 104 and 106 can be receivers or transmitters,etc., that can receive data from the PU component 102 and/or transmitdata thereto. In addition, though not shown, PU component 104 canadditionally or alternatively communicate with PU component 106 and/orvice versa.

The portion of the frequency band utilized for communication can bereserved for the PU components 102-106. In one example, the spectrum canbe reserved by a government agency (such as the Federal CommunicationsCommission (FCC), etc.), standards organization, and/or the like. Thefrequency band, however, can be utilized by other secondary devices aswell, in one example, such as a CR, devices communicating therewith,and/or other devices. This can be mandated by the same governmentagency, standards organization, etc., in one example. Secondary devices,however, can determine whether a portion of the frequency band iscurrently utilized by a PU to avoid interfering with the primaryreserved use and/or avoid receiving interference from the PUs as part ofthe mandate.

For this reason and other cases where determining utilized andunutilized frequency bands is beneficial, a spectrum sensing component108 is also provided that can detect presence of communication over afrequency band and/or identify whether the communication is by PUs,secondary users (SU), etc. As described further below, the spectrumsensing component 108 can determine one or more signals of interest(SOI) from an antenna array measurement related to the various PUcomponents 102-106. The spectrum sensing component 108 can furtherdetermine whether a related communication channel is occupied by a PU,SU, or is vacant based at least in part on the SOIs. In one example, asdescribed further herein, the spectrum sensing component 108 can utilizecyclostationary beamforming to acquire the SOI, and determine a sourceof the SOI as a PU, SU, or other noise based on detecting one or moremainlobes and/or sidelobes in the SOI. Cyclostationary beamforming canrefer to extracting a signal (e.g., as a single beam) from a frequencyband at a unique cycle frequency. For example, a mainlobe refers to alargest lobe in the frequency band, and a sidelobe refers to a lobe inthe spectrum that is not the mainlobe. In an example, thecyclostationary beamforming can be implemented according to aself-coherent restoral (SCORE) algorithm, such as adaptive cross-SCORE(ACS), adaptive phase-SCORE (APS), least squares SCORE (LS-SCORE),cross-SCORE, auto-SCORE, cyclic adaptive beamforming (CAB), adaptive CAB(ACAB), and/or the like.

In one example, detection of whether the spectrum is currently occupiedby a PU can be stated by a binary hypothesis test. A null hypothesis H₀corresponds to the absence of a signal, and a hypothesis H₁ correspondsto the presence of a signal. The signal received by the spectrum sensingcomponent 108, x(t), can be given by

${x(t)} = \left\{ \begin{matrix}{{w(t)},} & H_{0} \\{{{{hs}(t)} + {w(t)}},} & H_{1}\end{matrix} \right.$where s(t) is the PU signal, h is the amplitude gain of the channel, andw(t) is the additive white Gaussian noise (AWGN) with zero mean andvariance σ_(n) ². Given a decision statistic d, the probabilities ofdetection P_(d), false alarm P_(fa), and missed alarm P_(m) are,respectively, given byP _(d) =E[Pr(H ₁ |H ₁)]=Pr(d>d _(th) |H ₁)P _(fa) E[Pr(H ₁ |H ₀)]=Pr(d>d _(th) |H ₀)P _(m) =E[Pr(H ₀ |H ₁)]=1−P _(d)where d_(th) is a threshold level, which can be calculated from aspecified P_(fa). Naturally, P_(fa) is independent of the signal tonoise ratio (SNR), since under the H₀ hypothesis there is no PU signalpresent. Conversely, P_(d) is dependent on the SNR of the receivedsignal as well as the channel conditions.

From the incumbent protection point of view, a higher P_(fa) is moretolerable than a lower P_(d). For example, in Institute of Electricaland Electronics Engineers (IEEE) 802.22, P_(d)=0.9 is chosen for the SNRof −20 dB. Note that if the PUs require 100% protection in its frequencyband, SUs cannot communicate in that frequency band. In view of theabove formulas and considerations, the spectrum sensing component 108,which can be related to a SU, can detect occupancy and identity of oneor more SOIs, as described further herein. As mentioned, the detectioncan be based at least in part on evaluating one or more cyclostationaryproperties of the SOIs in view of the formulas and/or considerations. Inaddition, in one example, the spectrum sensing component 108 can performsuch detection while wirelessly transmitting signals.

Turning to FIG. 2, a block diagram of an example CR 200 in accordancewith various aspects is illustrated. The CR 200, as described, can beemployed in a variety of environments where it can communicate withvarious devices in frequency bands reserved for disparate devicescommunicating using disparate technologies, such as PUs of the frequencyband. In this regard, the CR 200 can communicate in portions reservedfor but not utilized by surrounding PUs to provide efficient use ofspectrum resources. To this end, the CR 200 comprises a spectrum sensingcomponent 108 that analyzes frequency bands to determine existenceand/or identification of PUs communicating over the spectrums, acognition management component 202 that selects resources over thefrequency band for communication based at least in part on determinedexistence/identifications of PUs by the spectrum sensing component 108,a control action component 204 that communicates over the selectedresources and/or notifies other devices or radios that it is utilizingthe selected resources, and a transmitter/receiver component 206 thatfacilitates communicating with one or more disparate CRs or otherwireless devices.

In one example, the spectrum sensing component 108 can determine one ormore resources of a frequency band over time that are reserved for butnot being utilized by a PU. Based on this information, the cognitionmanagement component 202 can select the one or more resources forcommunicating with disparate CRs (not shown) or other devices usingdynamic spectrum management and/or the like. It is to be appreciatedthat the cognition management component 202 can additionally providequality-of-service provisioning at the transmitter/receiver component206. In another example, the disparate CRs or other devices candetermine the resources and notify the CR 200 to utilize the resourcesto communicate with the disparate radio or device. The control actioncomponent 204 can facilitate communicating with disparate radios ordevices over the resources of frequency band in view of the above, forexample. In addition, the control action component 204 can providetransmit-power control (TPC), adaptive modulation and coding (AMC), ratecontrol, etc., at the transmitter/receiver component 206 or relatedcomponents.

It is to be appreciated that resources of frequency band not beingutilized by the PU can subsequently become utilized by the PU. In thiscase, the cognition management component 202 can detect interferencefrom the PU and cause the spectrum sensing component 108 to determineother resources of the same or a different spectrum for communicating.The control action component 204 can accordingly utilize the determinedresources and/or notify one or more disparate CRs of the switch inresources. In addition, as described further herein, thetransmitter/receiver component 206 can communicate with one or moredisparate devices while the spectrum sensing component 108simultaneously measures the frequency band, so long as the transmittedsignal has a different cycle (or conjugate cycle) frequency.

Spectrum sensing functionality in the spectrum sensing component 108 canbe divided into two subtasks: occupancy sensing and identity sensing.Spectrum sensing schemes performed by the spectrum sensing component 108can be either reactive or proactive, depending on how they search forwhite spaces (e.g., unused frequency bands). Reactive schemes canoperate on an on-demand basis where the CR 200, or one or more relatedcomponents, starts to sense the spectrum only when it has some data totransmit. Proactive schemes, on the other hand, can minimize realizeddelay of the spectrum sensing component 108 by finding an idle bandthrough maintaining a list of licensed bands currently available foropportunistic access through periodic spectrum sensing at the spectrumsensing component 108.

In one example, the spectrum sensing component 108 can utilize radiosignal analysis to detect and/or identify a user of frequency bandresources. For radio signal analysis, modulation recognition and bitstream analysis can be applied to identify whether an alarm (e.g., adetected signal) corresponds to a PU, or a SU, or noise (e.g., falsealarm). Modulation recognition can be necessary for the selection of asuitable demodulation process at the receiver. Knowledge of the types ofservice operating on a channel can assist the decision of jumpingchannels in a way which minimizes overhead to the CR 200 and its impacton the PUs of the spectrum. Also, the cognition management component 202can recognize other CRs on the link channel to prevent sensing oneanother as PUs and accordingly jumping frequencies.

In one example, the spectrum sensing component 108 can extract a numberof features to identify the type of the PUs from the received data usingsignal processing techniques. These features can be frequency-domainfeatures (e.g., bandwidth, center frequency, single carrier versusmulti-carrier), time-domain features (e.g., maximum duration of asignal, multiple-access technique, duplexing technique, frame duration,spreading codes or hopping patterns), and/or the like. Some or all ofthe features can be extracted from the received data and used forclassification. The spectrum sensing component 108 can identify the PUsby using the a priori information about related transmission parameters.In this regard, the spectrum sensing component 108 can employ aclassifier, such as the optimal Bayesian classifier, a neural networkclassifier, and/or the like. A classifier can be trained off-line, butthe recognition process can be performed online by the spectrum sensingcomponent 108 on the incoming signal at an affordable complexity.

Spectrum management functions address four major challenges: spectrumsensing, spectrum decision, spectrum sharing, and spectrum mobility.Spectrum mobility allows a CR to exchange its frequency of operation ina dynamic manner by allowing the CRs to seamlessly operate in the bestavailable frequency band. Spectrum sharing deals with fair spectrumscheduling, which is a media access control (MAC) functionality. Thespectrum sensing component 108 of the CR 200, as described, can tomaintain an up-to-date list of available channels within a band. Thechannel usage database can also be used to avoid the occupied licensedchannels, and the cognitive management component 202 can estimate itsposition and check a database to find out which channels are vacant inits vicinity.

The cognitive management component 202 selects a set of subchannels fromthe PU band to establish a SU link that adapts itself in accordance withthe PU spectral activity on that band. The CR 200 is required to vacatea subchannel as soon as a PU becomes active on that subchannel. Thiscauses the CR 200 to lose packets on that subchannel. To compensate forthis loss, the transmitter/receiver component 206 can utilize a class oferasure correction codes called LT (Luby transform) codes or digitalFountain codes for packet-based channels with erasures beforetransmitting SU packets on these subchannels, for example. This canprovide packet-level protection at the transport layer or higher,augmenting the bit-level protection that may be provided by the MAC andphysical layers.

Turning to FIG. 3, a block diagram of an example system 300 forevaluating frequency bands for SU communication is shown. In particular,a spectrum sensing component 108, as described herein, is providedcomprising a signal receiving component 302 that receives one or moresignals over a portion of a frequency band in a wireless communicationsenvironment, a cyclostationary beamforming component 304 that calculatesa signal from the portion of the frequency band by using acyclostationary beamforming algorithm, and a signal identificationcomponent 306 that detects a source of a signal in the portion of thefrequency band. In addition, a PU component 102 is shown thatcommunicates over an assigned frequency band or portion thereof alongwith a SU component 308 that communicates in the same frequency band, orportion thereof, during time intervals when the PU component 102 is notcommunicating and/or on frequencies within the spectrum, but adjacent tothose utilized by the PU component 102.

According to an example, the signal receiving component 302 can obtainone or more signals over a frequency band, or portion thereof, which canhave been transmitted by the PU component 102 and/or SU component 308.The one or more signals can be received as a result of the signalreceiving component 302 measuring an antenna array. In one example, asdescribed, this measurement can be performed to determine whether thefrequency band or related portion can be utilized for communicating by aCR or other SU device related to the spectrum sensing component 108. Thecyclostationary beamforming component 304 can extract a SOI from theantenna array measurement using cyclostationary beamforming, in oneexample. A cyclostationary beamforming algorithm, such as ACS, cananalyze a unique cycle frequency, which can be determined based on acarrier frequency, symbol rate, and/or other signal properties. In thisregard, the cycle frequency can be communicated to the cyclostationarybeamforming 304 based on one or more known specifications related to PUsof the frequency band, discerned from patterns of signals received overthe frequency, specified by one or more disparate devices or components,and/or the like.

For example, man-made modulated signals can be coupled with sinewavecarriers, pulse trains, coding, repeating spreading, hopping sequencesor cyclic prefixes, resulting in built-in periodicity. These modulatedsignals are characterized as second-order cyclostationary if their meanand autocorrelation display periodicity. For cyclostationary signals,non-overlapping frequency bands are uncorrelated, and further, theinherent periodicity implies some spectral redundancy, which results incorrelation between non-overlapping spectral components separated bysome multiple of the cycles.

In the time domain, a second-order cyclostationary process is a randomprocess for which the statistical properties (namely, the mean andautocorrelation) change periodically as functions of time, with a periodT.m _(x)(t)=m _(x)(t+T)∀tR _(xx)(t ₁ ,t ₂)=R _(xx)(t ₁ +T,t ₂ +T)∀t ₁ ,t ₂Since R_(xx)(t₁, t₂) is periodic, it has a Fourier-seriesrepresentation. By denoting

${t_{1} = {{t + {\frac{\tau}{2}\mspace{14mu}{and}\mspace{14mu} t_{2}}} = {t - \frac{\tau}{2}}}},$such a Fourier series is as follows

${R_{xx}\left( {{t + \frac{\tau}{2}},{t - \frac{\tau}{2}}} \right)} = {\sum\limits_{\alpha}{{R_{xx}^{\alpha}(\tau)}{\mathbb{e}}^{j\; 2\;\pi\;\alpha\; t}}}$where the Fourier coefficients are R_(xx) ^(α)(τ), which is called thecyclic autocorrelation function or spectral correlation function, and αis known as the cycle frequency. A communication signal received by thesignal receiving component 302 can have cycle frequencies that arerelated to the carrier frequency, the symbol rate and its harmonics, thechip rate, guard period, the scrambling code period, and the channelcoding scheme, for example.

A scalar waveform x(t) is said to be spectrally self-coherent (orconjugate self-coherent) at a frequency α, if the spectral correlationfunction, that is, the correlation between x(t) and x(t) shifted infrequency by α, is nonzero for some delay τ

${R_{{xx}^{{(*})}}^{\alpha}(\tau)} = {\left\langle {{{x\left( {t + \frac{\tau}{2}} \right)}\left\lbrack x^{*} \right\rbrack}^{{(*})}\left( {t - \frac{\tau}{2}} \right){\mathbb{e}}^{j\; 2\;\pi\;\alpha\; t}} \right\rangle_{\infty} \neq 0}$where * is the conjugate operator, the optional conjugation (*) isapplied in the conjugate self-coherence case, <•>_(∞) denotes infinitetime-averaging, j is the imaginary number, and α is the non-conjugate orconjugate cycle frequency. If a signal is cyclostationary with period T,then cyclic autocorrelation has a component at α=1/T. For stationarysignals, R_(xx) _((*)) ^(α)=0 for any α≠0.

As mentioned, the cyclostationary beamforming 304 can utilize acyclostationary beamforming algorithm to detect signals present in afrequency band or portion thereof. Some examples of such algorithmsinclude LS-SCORE, cross-SCORE, auto-SCORE, etc., as described. In anexample, however, the cyclostationary beamforming 304 uses an ACSalgorithm to perform cyclostationary beamforming, extracting a number ofsignals from co-channel interference with only knowledge of cyclefrequencies thereof, which can be assumed to be different. In addition,the ACS algorithm is applicable to cyclostationary and conjugatecyclostationary signals.

For narrowband signals, when an antenna array is excited by a SOI s(t),background noise, and co-channel interference, the received signal atthe array, which can include signals from the PU component 102 and/or SUcomponent 308, can be expressed asx=ds(t)+i(t)where d is the steering vector of the SOI, and i(t) is the sum of theinterfering signals and the background noise. Assume that s(t) isspectrally self-coherent at a, and that i(t) is not spectrallyself-coherent at α and is temporally uncorrelated with s(t). Thebeamformer is defined asγ(t)=w ^(H) x(t)where w is the beamforming weight and y(t) is the extracted SOI. Areference signal r(t) is defined asr(t)=c _(H) u(t)where c is a control vector, and u(t) is x⁽*⁾(t) shifted in frequency byα and in time by τu(t)=x ⁽*⁾(t−τ)e ^(j2παt)

The ACS algorithm optimizes the same objective as the cross-SCOREalgorithm does, but implements in a different way. It maximizes thestrength of the spectral cross-correlation (or conjugatecross-correlation) coefficient ρ_(yr) ^(α) between the beamformer outputy(t) and the reference signal r(t)

$w,{c = {{\arg\;{\max\limits_{w,c}{{{\hat{\rho}}_{y\; r}^{\alpha}(\tau)}}^{2}}} = \frac{{{w^{H}{\hat{R}}_{xu}c}}^{2}}{\left\lbrack {w^{H}{\hat{R}}_{xx}w} \right\rbrack\left\lbrack {c^{H}{\hat{R}}_{uu}c} \right\rbrack}}}$where {circumflex over (R)}_(xu), {circumflex over (R)}_(xx),{circumflex over (R)}_(uu) are the estimated correlation matrices. Thiscan be transformed into maximizing the numerator while fixing thedenominator, that is,

$w,{c = {\arg\;{\max\limits_{w,c}{{w^{H}{\hat{R}}_{xu}c}}^{2}}}}$s.t.w^(H)R̂_(xx)w = 1,  c^(H)R̂_(uu)c = 1By applying the Lagrange multiplier method and implementing somemanipulation,λw={circumflex over (R)} _(xx) ⁻¹ {circumflex over (R)} _(xu) cλc={circumflex over (R)} _(uu) ⁻¹ {circumflex over (R)} _(xu) w

Unlike the cross-SCORE that searches the dominant mode at each sample,the ACS solves one eigenvalue problem for all the samples. Thissubstantially reduces the total number of complex multiplications from(6.75n²+4.25n)m to 6.75n²+4.25n for each sample, where m is the numberof iterations needed for solving the eigenvalue to a specified accuracyfor each sample of the cross-SCORE algorithm. For slow fading channels,the ACS algorithm is given by

w(k) = R̂_(xx)⁻¹(k)R̂_(xu)(k)c(k − 1) ${w(k)} = \frac{w(k)}{{w(k)}}$c(k) = R̂_(uu)⁻¹(k)R̂_(ux)(k)w(k) where${{\hat{R}}_{xu}(k)} = {\frac{k - 1}{k}\left\lbrack {{{\hat{R}}_{xu}\left( {k - 1} \right)} + {\frac{1}{k - 1}{x(k)}{u^{H}(k)}}} \right\rbrack}$R̂_(ux)(k) = R̂_(xu)^(H)(k)${{\hat{R}}_{xx}^{- 1}(k)} = {\frac{k}{k - 1}\left\{ {{{\hat{R}}_{xx}^{- 1}\left( {k - 1} \right)}\frac{{{\hat{R}}_{xx}^{- 1}\left( {k - 1} \right)}{x(k)}{x^{H}(k)}{{\hat{R}}_{xx}^{- 1}\left( {k - 1} \right)}}{\left( {k - 1} \right) + {{x^{H}(k)}{{\hat{R}}_{xx}^{- 1}\left( {k - 1} \right)}{x(k)}}}} \right\}}$R̂_(uu)⁻¹(k) = [R̂_(xx)⁻¹(k)]^((*))

By specifying {circumflex over (R)}_(xx) ⁻¹(1), the iteration canproceed. {circumflex over (R)}_(xx) ⁻¹(1) can be selected by averaging Msnapshots of the frequency band, received by the signal receivingcomponent 302, (M>n_(a)), n_(a) being the number of antenna elements,

${{R_{xx}(1)} = {\frac{1}{M}{\sum\limits_{{- M} + 2}^{1}{{x({\mathbb{i}})}{x^{H}({\mathbb{i}})}}}}},$and R_(xx) ⁻¹(1)=[R_(xx)(1)]⁻¹. The performance of a beamformer ischaracterized by the output signal-to-interference-plus-noise ratio(SINR)

${S\; I\; N\; R} = \frac{w^{H}{dR}_{ss}d^{H}w}{w^{H}R_{I}w}$where R_(ss) is the autocorrelation or the average power of the SOI s(t)and R_(I) is the autocorrelation of the summed interference and noise.The cyclostationary beamforming 304 can use the above algorithm tooutput beamformed cyclostationary signals, from a frequency band, forevaluation and/or identification thereof.

For example, in a typical CR application, modulation parameters such asthe carrier frequencies, data rates, and bandwidths of the possiblechannels for PU signals (e.g., from PU component 102) are defined in astandard and can be known by CRs, as described with respect to thecognition management component 202 in previous figures. Each class of CRmay also know such modulation parameters of other classes (e.g., otherCRs, such as SU component 308). Typically, the transmission channels canbe specified as

${f_{c} = {f_{0} + {\left( {n - \frac{1}{2}} \right)B}}},\mspace{14mu}{n = 1},2,\ldots\mspace{11mu},N$where f₀ is the start frequency of the band, B is the bandwidth of eachchannel, and N defines the number of channels. This is also applicablefor OFDM signals. One or more co-channel signals may be present on eachchannel, as in the spread-spectrum communication scenarios. A CR can berequired to find a vacant channel with the carrier frequency f_(c) andthe bandwidth B (e.g., utilizing a spectrum sensing component 108, asshown) before accessing the network. The spectrum sensing component 108can test all the channels for the presence of transmission. Thecyclostationary beamforming 304 can be leveraged, in this regard, toperform the following procedure for beamforming cyclostationary signals.

ŷ(k) = ACS (α, opmode, N_samples, x(k)) Input: α-non-conjugate orconjugate cycle frequency opmode-non-conjugate or conjugatecyclostationary mode N_samples-number of samples x(k)-samples at theantennas Output: ŷ(k)-beamforming output begin procedureα_(n) := α/f_(s),  τ_(n) := 0${R_{xx}(0)}:={\frac{1}{M}{\sum\limits_{{- M} + 1}^{0}{{x(i)}{x^{H}(i)}}}}$R_(xx)⁻¹(0) := [R_(xx)(0)]⁻¹ R̂_(xu)(0) := O c(0) := rand(L, 1)for  k  to  N_samples, u(k) := x^((*))(k − τ_(n))e^(j 2 πα_(n)k)${{\hat{R}}_{xu}(k)}:={\frac{k - 1}{k}\left\lbrack {{{\hat{R}}_{xu}\left( {k - 1} \right)} + {\frac{1}{k - 1}{x(k)}{u^{H}(k)}}} \right\rbrack}$R̂_(ux)(k) := R̂_(xu)^(H)(k)${{\hat{R}}_{xx}^{- 1}(k)}:={\frac{k}{k - 1}\left\{ {{{\hat{R}}_{xx}^{- 1}\left( {k - 1} \right)}\frac{{{\hat{R}}_{xx}^{- 1}\left( {k - 1} \right)}{x(k)}{x^{H}(k)}{{\hat{R}}_{xx}^{- 1}\left( {k - 1} \right)}}{\left( {k - 1} \right) + {{x^{H}(k)}{{\hat{R}}_{xx}^{- 1}\left( {k - 1} \right)}{x(k)}}}} \right\}}$R̂_(uu)⁻¹(k) := [R̂_(xx)⁻¹(k)]^((*)) w(k) := R̂_(xx)⁻¹(k)R̂_(xu)(k)c(k − 1)${w(k)}:=\frac{w(k)}{{w(k)}}$ c(k) := R̂_(uu)⁻¹(k)R̂_(ux)(k)w(k)ŷ(k) := w^(H)(k)x(k) end for end procedureIt is to be appreciated that other procedures are possible includingvariations of the above. In one example, the cyclostationary beamforming304 can perform substantially any procedure that beamformscyclostationary signals, as described above.

Based at least in part on output from the cyclostationary beamforming304, the signal identification component 306 can detect sources of theoutput signals according to various mechanisms, such as learning,determining or receiving features present in such signals. In oneexample, the signal identification component 306 can detect the signalsources according to the following procedure. It is to be appreciatedthat 1e6 in the procedure can be substantially any sufficiently largenumber, in one example.

begin procedure  for n = 1 to N (all possible channels)   for l = 1 toN_(PU) (all PU modes)    isHole := 0; isPU := 0; isSU := 0;    Set cyclefrequency for PUs, α_(PU)    Call procedure ACS (above), and extract theSOI ŷ(k) at α_(PU) .    Calculate the power spectrum of ŷ using FFT.   Test the occupancy of channel n by analyzing the power spectrum:    if there is a mainlobe in channel n ,      channel n is occupied asa PU signal in mode l .      isPU := isPU + 1e6; (occupied by PU)     break;     elseif there is no lobe in channel n (for thresholdd_(n)),      isHole := isHole + 2;     elseif there is a lobe in channeln and other lobes in other     channels,      Test SU signals in channeln :      for m = 1 to M (all possible SU types)       Set α_(SU) ;      Call procedure ACS, and extract the SOI ŷ′(k) at α_(SU) ;      Calculate the power spectrum of ŷ′(k);       Test the powerspectrum:        if there is a mainlobe in channel n ,         isSU :=isSU + 1e6; (occupied by SU)         break;        elseif there is nolobe in channel n (for threshold d_(n)),         isHole := isHole + 2;       else         isHole := isHole+1; isPU := isPU+2;        end if     end for     end if     if (isPU>isSU) and (isPU>isHole),     channel n is occupied by a PU;     elseif (isSU>isPU) and(isSU>isHole),      channel n is occupied by a SU;     else      channeln is a hole;     end if   end for  end for; end procedure

The threshold d_(n) can be defined as several times the noise band inthe channel. To differentiate between signals from the PU component 102and SU component 308, their respective conjugate or non-conjugate cyclefrequencies can be selected to be different. Most other existingspectrum sensing techniques perform in-band sensing and measurementduring the specified quiet periods in order to avoid interference fromthe network itself. Using the above procedure, the cyclostationarybeamforming 304 and signal identification component 306 can measurewhile a related CR is transmitting, as described, so long as thetransmitted signal does not have the same cycle frequency.

The above procedure is also advantageous over spectrum cyclicanalysis-based detection approaches, since the latter has a much highercomplexity due to computation of the spectrum cyclic density (SCD)function. In spectrum cyclic analysis-based approaches, for example,detection of the specific feature requires sufficient over-sampling andminimum resolution in both frequency and cycle domains. The signal hasto be over-sampled in the cycle domain such that the Nyquist rate formaximum resolvable cycle frequencies is satisfied. The resolutions infrequency and cycle domains are improved by observing the signal over along period of time, that is, over many symbol periods. Search for thepeaks on the SCD function is also computationally complex. For the aboveprocedure, since the modulation and coding of the PU component 102 andSU component 308 signals have been defined in their standards, the cyclefrequencies for each PU component 102 and SU component 308 mode on eachchannel are known and usually are designed to be unique, if the channelis occupied by PU component 102, CR, or other SU component 308. Thedetection depends on the ACS algorithm utilized by the cyclostationarybeamforming 304 and the extracted SINR, as shown above.

Referring to FIG. 4, an example system 400 that facilitates cooperativespectrum sensing is illustrated. PU components 102-106 are provided thatcommunicate over a reserved frequency band, or portion thereof, asdescribed. In addition, a SU component 308, which can be a CR, astationary device, and/or the like, is shown. The SU component 308comprises a spectrum sensing component 108 that determines portions ofthe frequency band over which the PU components 102-106 and/or othercomponents are not communicating, as described. A common receivercomponent 402 is also provided that comprises a spectrum informationcomponent 404 that receives spectrum information from one or more CRs orother SU components and an information sharing component 404 thatcommunicates the unutilized frequency band portions to one or more CRs,SU components, etc. It is to be appreciated that the common receivercomponent 402 can make independent spectrum measurements, in oneexample, for transmission using the information sharing component 406.The SU component 308 additionally comprises an information receivingcomponent 408 that can obtain information of one or more unutilizedfrequency band portions from the information sharing component 406.

In an example, spectrum sensing components 108 of multiple SU componentscan make a binary decision based on local measurement, and then forwardone bit of the decision to the common receiver component 402, where allone-bit decisions can be fused according to an OR logic. In analternative example, each spectrum sensing component 108 can forward itsmeasurement to the common receiver component 402. A hard decisionapproach can perform almost as well as a soft decision one in terms ofdetection performance, but it needs a low bandwidth control channel. Toreduce the overhead due to sending the decisions from the informationsharing component 406, censoring can be applied by not sending thoseuncertain decisions. In case that the common receiver component 402makes final decision on the K binary decisions using an OR rule, theprobabilities of false alarm and missing detection for K decisions arederived as

$\begin{matrix}{P_{fa} = {\Pr\left( H_{1} \middle| H_{0} \right)}} \\{= {1 - {\Pr\left( H_{0} \middle| H_{0} \right)}}} \\{= {1 - {\prod\limits_{i = 1}^{K}\;\left( {1 - P_{{fa},i}} \right)}}}\end{matrix}$$P_{m} = {{\Pr\left( H_{0} \middle| H_{1} \right)} = {\prod\limits_{i = 1}^{K}\; P_{m,i}}}$where P_(fa,i) and P_(m,i) denote the false alarm and miss probabilitiesof the i th spectrum sensing component 108 in its local spectrumsensing. Assuming that each spectrum sensing component 108 achieves thesame P_(fa,0) and P_(m,0), then P_(m)=P_(m,0) ^(K), and K can be treatedas the sensing diversity order, which is provided by the space diversityof the multiple spectrum sensing components 108. The information sharingcomponent 406 can transmit the spectrum information to one or more SUcomponents, such as SU component 308 or other components, CRs, and/orthe like. The SU component 308 can receive the spectrum information viathe information receiving component 408 and utilize the information inselecting one or more frequency band portions for communicating withother devices.

When a SU component 308 (e.g., CR) is far from a PU, cooperativespectrum sensing allows two SU components 308 to cooperate by treatingthe SU that is close to the PU as a relay. This achieves a diversitygain arising from relay, which is based on either theamplify-and-forward (AF) or decode-and-forward (DF) cooperativeprotocol. One of the SU components acts as a relay for the other,resulting in lower outage probabilities. This can effectively combatshadowing and the hidden terminal problem.

When two SU components, such as SU component 308, are in closeproximity, they can be used as a virtual antenna array; that is, themeasurements of the two SU components are exchanged, and the two SUcomponents then jointly transmit using the Alamouti space-time code tocombat fading. Multiuser diversity is a form of selection diversity inwhich the user with the highest SNR is chosen as the transmission link.Multiuser diversity can be exploited in cooperative spectrum sensing torelay the sensing decision of each SU component to the common receivercomponent 402. This helps to reduce the reporting error probability, inone example.

Referring now to FIG. 5, a methodology that can be implemented inaccordance with various aspects described herein is illustrated. While,for purposes of simplicity of explanation, the methodology is shown anddescribed as a series of blocks, it is to be understood and appreciatedthat the claimed subject matter is not limited by the order of theblocks, as some blocks may, in accordance with the claimed subjectmatter, occur in different orders and/or concurrently with other blocksfrom that shown and described herein. Moreover, not all illustratedblocks may be required to implement the methodology in accordance withthe claimed subject matter.

Furthermore, the claimed subject matter may be described in the generalcontext of computer-executable instructions, such as program modules,executed by one or more components. Generally, program modules includeroutines, programs, objects, data structures, etc., that performparticular tasks or implement particular abstract data types. Typicallythe functionality of the program modules may be combined or distributedas desired in various embodiments. Furthermore, as will be appreciatedvarious portions of the disclosed systems above and methods below mayinclude or consist of artificial intelligence or knowledge or rule basedcomponents, sub-components, processes, means, methodologies, ormechanisms (e.g., support vector machines, neural networks, expertsystems, Bayesian belief networks, fuzzy logic, data fusion engines,classifiers . . . ). Such components, inter alia, can automate certainmechanisms or processes performed thereby to make portions of thesystems and methods more adaptive as well as efficient and intelligent.

Referring to FIG. 5, a methodology 500 that facilitates sensing one ormore devices communicating in a frequency band is illustrated. At 502,an antenna array can be measured over a frequency band. Multipleantennas in the array can receive signals in the frequency band that canbe transmitted by various wireless devices (e.g., PUs and SUs, asdescribed). At 504, one or more SOIs can be extracted from the antennaarray measurement using cyclostationary beamforming. As described above,the beamforming can be performed using an ACS or other algorithm thatoutputs beamformed signals. This facilitates enhanced identification ofthe SOIs, such as by evaluating lobes in the SOIs.

At 506, it can be determined whether the frequency band is beingutilized by a PU, SU, or is vacant, based on the one or more SOIs. Forexample, as described, if the SOI is a conjugate or non-conjugate cyclefrequency related to a PU and has a mainlobe, then it can be assumedthat a PU is communicating over the related frequency band. If there isa sidelobe, along with other lobes in other channels, then the frequencyband can be evaluated to determine if there are mainlobes in theconjugate or non-conjugate cycle frequencies related to the SOIs ofknown SUs. If there are mainlobes, then it can be assumed that a SU iscommunicating over the related frequency band. If not, then it can beassumed that the frequency band is vacant, for example. It is to beappreciated that the conjugate or non-conjugate cycle frequenciesrelated to the PU and/or SU can be received from one or more disparatedevices, hardcoded according to a specification, and/or the like, asdescribed. At 508, a portion of the frequency band can be selected forcommunicating based on whether the frequency band is utilized by a PU,SU, or is vacant.

Turning now to FIGS. 6-15, various graphs are depicted presentingsimulated results of an example application utilizing an ACS algorithmto detect and/or identify signals in a frequency band. In the graphs, itcan be assumed that the entire spectrum is divided into a fixed numberof ten channels at carrier frequencies 2001.1, 2002.1, . . . , 2010.1MHz. A uniform linear array with n=8 antenna elements is used. Thespacing between adjacent elements is half the wavelength at the carrierfrequency of 2 GHz. The standard deviation of the noise at the array isσ_(n) ²=0.1. The signal environment for benchmarking is shown in thetable below: there are 5 PU signals representing a primary service, and2 SU signals representing different CR modes. The sampling rate f_(s) atthe receiver is chosen to be 20 Million samples per second (Msps), andall signals are at the same noise power level σ_(s) ²=0.01, and thesignal power can be obtained from

${SNR} = {\frac{P_{s}}{\sigma_{s}^{2}}.}$The signals are BPSK or 16QAM signals, which are raised-cosine filteredwith a roll-off factor of 0.25.

Carrier SNR Signal (MHz) f_(baud)/(f_(s)/20) Modulation DoA (dB) PU/SU A2001.1 1/4 BPSK 30° 15 PU B 2002.1 1/4 BPSK 20° 25 PU C 2006.1 1/4 BPSK−15° 30 PU D 2007.1 1/4 BPSK −30° 10 PU E 2008.1 1/4 BPSK 55° 20 PU F2005.1 1/7 16QAM −40° 5 SU G 2009.1  1/11 16QAM 25° 15 SUFor these modulations, the maximum self-coherence occurs at τ=0, and τ=0is selected. The BPSK signal has conjugate cycle frequency atα=±2f_(c)+mf_(baud), m=0, ±1 . . . , and has cycle frequency atα=mf_(baud), m=±1, ±2, . . . . In a multiple signal environment, thesignals are designed so that their selected cycle frequencies shouldhave a least common multiple that is as large as possible. The 16QAMsignal has only non-conjugate cyclostationarity with cycle frequency atα=mf_(baud), m=±1, ±2, . . . . The ACS algorithm can be implementedequally well for both non-conjugate and conjugate cyclostationarysignals, depending on the properties of the desired signals.

It is to be appreciated that the SNR of the signal itself has asignificant impact on the beamforming algorithms and the noise containedin the signal itself damages the cyclostationary property of the signal.So in FIGS. 6-15, the SNRs of the signals are to be above 5 dB. However,the noise at the receiver can be very large. The received SNR at thereceiver can be very small, (e.g., at −20 dB). The assignment of carrierfrequencies and the selection of (conjugate) cycle frequencies must becareful. When signal D is selected as the SOI, by setting the conjugatecycle frequency as α=2×f_(c)+f_(baud) Hz for the ACS algorithm, the PUsignal can be extracted, and the SINR performance and the power patternat the 10⁴th sample, as shown in FIG. 6. At 600, the graph depictssignal D (10 dB) selected as the SOI, which is a weak one among the 7signals. It is shown, at 604, that the ACS algorithm can effectivelyextract the desired signal, but the CAB algorithm at 606 fails, withoutfiltering the other signals in the 10 MHz band. At 602, the relatedpower beampattern is depicted showing beampattern for the ACS algorithmat 608 and for the CAB algorithm at 610.

The spectrums of the received SOI, original SOI, and extracted signalsusing the ACS and CAB algorithms are shown in FIG. 7 respectively at700, 702, 704, and 706. The spectrum is downconverted by 2 GHz to thebaseband. It is shown that at 7.1 MHz (which corresponds to 2007.1 MHz)the ACS-extracted signal 704 has a spectrum peak at 710, which ispresent in the original signal 702 at 708, while the CAB-extractedsignals at 706 have no peak at this location. Thus, the ACS caneffectively identify that the channel centered 2007.1 MHz is occupied bya PU. Using conjugate cyclostationary based algorithms withα=2f_(c)+f_(baud) to detect the spectrum occupancy by the PU signals onall the channels, the SUs cannot be reliably detected, since the SUsignals do not have conjugate cyclostationary property and both the ACSand CAB do not converge. The SINR performances of both the ACS and CABcan be undesirable, in an example. The extracted signal may typicallyhave spectrum peaks at all the frequencies of the original signals.

For example, at f_(c)=2005.1 MHz, the spectrum of the extracted signalis shown in FIG. 8, with the SOI received at 800, the original SOI at802, the ACS-extracted signal at 804, and CAB-extracted signal at 806.The ACS algorithm may sometimes generate a spectrum sidelobe at f_(c),shown at 810 and/or 812, though the original SOI at 802 can have aspectrum peak at 808, while the CAB algorithm most typically produces aspectrum null on this channel. From the ACS-extracted signal at 804, itcan be identified that the channel is not occupied by a PU but it may beoccupied by a SU. Since the SU signals are of 16QAM type, the SUoccupancy can be further tested by using the cyclostationary-based ACSalgorithm. For signal F, if the ACS at cycle frequency α=f_(baud)=1/7f_(s) is applied, the spectrum of the extracted signal is plotted inFIG. 9, with the SOI received at 900, the original SOI at 902, theACS-extracted signal at 904, and CAB-extracted signal at 906. Onceagain, the ACS can extract signal F shown at 910, and represented in theoriginal signal 902 at 908, but the CAB at 906 fails.

The corresponding SINR performance and the power pattern at the 10⁴thsample are shown in FIG. 10 at 1000, and the power beampattern at 1002.Thus, the ACS algorithm, shown at 1004, has better performance than theCAB algorithm, shown at 1006. The beampattern for the ACS algorithmrelates to the curve at 1008, and the CAB to the curve at 1010. Thus, asdescribed herein, the ACS algorithm proposed above is used forcyclostationary beamforming. The ACS algorithm generally converges ataround 2000 samples when the signal-to-interference-ratio (SIR) γ is −20dB or less. The number of samples required, N, should scale at betweenO(1/γ) and O(1/γ²). That is, the minimum number of required samples isless than that required for an energy detector.

FIGS. 11-13 relate to implementing Monto Caro simulation for PUdetection using the proposed algorithm. In this signal environment,conjugate cyclostationary beamforming is employed for PU detection withα=2f_(c)+f_(baud), and cyclostationary beamforming with α=f_(baud) forSU detection. The ACS algorithm is implemented for 5000 samples with aFFT length of 1024. As an initial implementation, conjugatecyclostationary-based ACS is utilized with α=2f_(c)+f_(baud) to detectthe PUs; non-conjugate cyclostationary-based ACS for SU detection is notimplemented so as to substantially reduce the computational cost, sinceit can be appreciated that the PU detection is more critical for CRs.For spectrum occupancy decision, if there is a mainlobe on the channelcentered at f_(c), the channel is occupied by a PU; if there is asidelobe on the channel centered at f_(c), it is occupied by a SU; ifthere is no lobe on the channel (assuming the peak in the channel isless than 4 times the mean power in the band), it is judged as aspectrum hole (e.g., vacancy as described herein). The result is shownin FIG. 11. It is shown that the probability for correct detection of PUis relatively good, but the probability of correct detection of SU isnot satisfactory.

The results are shown in FIG. 11 at graphs 1100, 1102, 1104, and 1106,where σ_(a) ²/σ_(s) ² are used to characterize the SNR. In particular,at graph 1100, the line at 1108 represents probability of a hole (orvacancy) being detected, the line at 1110 represents probability that ahole is missed, and the line at 1112 represents probability that thereis a false alarm detected. Similarly, at graphs 1102, 1104, and 1106,the lines at 1114, 1120, and 1126 respectively represent probability ofa SU, PU, and PU and SU are detected, the lines at 1116, 1122, and 1128respectively represent probability that a SU, PU, and PU and SU aremissed, and the lines at 1118, 1124, and 1130 respectively representprobability that there is a false alarm detected. The results aregenerally unsatisfactory. This is because some PU signals may be treatedas SU signals, if the ACS-extracted generates a sidelobe rather than amainlobe on the channel. Many channels occupied by SU signals are alsotreated as spectrum holes, since the SU signals do not have conjugatecyclostationary property and the algorithm cannot extract the signal onthe channel. Thus, the results for SUs and spectrum holes are notreliable.

After applying the conjugate cyclostationary-based ACS atα=2f_(c)+f_(baud) at f_(c), if there is a spectrum sidelobe at thechannel, it can be either a PU or SU. By testing substantially all thepossible SU data rates using the cyclostationary-based ACS algorithmuntil a spectrum mainlobe at the channel occurs, a SU can be determined;otherwise, it is not a SU and can be judged as a PU signal or a hole.The threshold for spectrum occupancy can be lowered to 3 times of thepower mean in the band. The result is shown in FIG. 12 in the graphs at1200, 1202, 1204, and 1206. In particular, at graph 1200, the line at1208 represents probability of a hole (or vacancy) being detected, theline at 1210 represents probability that a hole is missed, and the lineat 1212 represents probability that there is a false alarm detected.Similarly, at graphs 1202, 1204, and 1206, the lines at 1214, 1220, and1226 respectively represent probability of a SU, PU, and PU and SU aredetected, the lines at 1216, 1222, and 1228 respectively representprobability that a SU, PU, and PU and SU are missed, and the lines at1218, 1224, and 1230 respectively represent probability that there is afalse alarm detected. For this example, assuming that the possible SUsignals are of type 16QAM with baud rates

${\frac{1}{7}f_{s}},\mspace{14mu}{\frac{1}{11}f_{s}},{{and}\mspace{14mu}\frac{1}{13}f_{s}},$the probability of correct detection of PU signals has been improvedover that shown in FIG. 11.

Energy detection is a simple and popular technique for spectrum sensing.It examines the signal power at a specified channel to judge theoccupancy of the channel. This method cannot discriminate between PU andSU signals. It cannot detect a signal if it is buried in noise. Channeloccupancy can be detected by bandpass-filtering a channel and thencalculating the autocorrelation of the measured signal. An alternativemethod is implemented in the frequency domain, by examining the spectrumpeak values at each channel. When the detection threshold is set as 6times of the mean power in each channel, the result is shown in FIG. 13in the graphs at 1300 and 1302. In particular, at graph 1300, the lineat 1304 represents probability of a hole (or vacancy) being detected,the line at 1306 represents probability that a hole is missed, and theline at 1308 represents probability that there is a false alarmdetected. Similarly, at graph 1302, the line at 1310 representsprobability of a PU and SU detected, the line at 1312 representsprobability that a PU and SU are missed, and the line at 1314 representsprobability that there is a false alarm detected. Note that for theenergy detection approach only one antenna is used and σ_(a) ² is thenoise power at the single antenna.

Compared to the result by the proposed approach in FIG. 12, for asimilar correct detection probability of channel occupancy (PU+SU), theprobability of correct detection of spectrum holes is relatively lowerin the energy detection approach; this corresponds to lower spectrumefficiency. By decreasing the detection threshold, the probability ofcorrect detection of occupied channels is increased to more closed to100%; this, however, further reduces the probability of correctdetection of spectrum holes, and hence the spectrum efficiency.

In addition, the proposed spectrum sensing approach has the capabilityof correctly identifying PU and SU signals, which cannot be accomplishedusing energy detection. In FIG. 12, the probability of correctlyidentifying the SU signal is much far from 100%; this is because one ofthe two SU (signal F) is too weak. Another advantage is that theproposed method can extract and sense substantially all the co-channelsignals on the same channel (f_(c)), as long as they have different avalues or cyclostationary properties. This property can be applied tospread-spectrum signals, but it requires each signals has different datarates or coding schemes. In contrast, the energy detection technique canonly identify that the channel is occupied, but it cannot identify thenature of the signals.

Finally, when checking the case that all the signals have the same lowpower (with a SNR of 10 dB, i.e., a signal power of 0.1), the resultsfor the proposed approach and the energy detection approach are shown inFIGS. 14 and 15 (for the detection threshold is 5 times of the meanpower in each channel), respectively. In particular, in FIG. 14, atgraph 1400, the line at 1408 represents probability of a hole (orvacancy) being detected, the line at 1410 represents probability that ahole is missed, and the line at 1412 represents probability that thereis a false alarm detected. Similarly, at graphs 1402, 1404, and 1406,the lines at 1414, 1420, and 1426 respectively represent probability ofa SU, PU, and PU and SU are detected, the lines at 1416, 1422, and 1428respectively represent probability that a SU, PU, and PU and SU aremissed, and the lines at 1418, 1424, and 1430 respectively representprobability that there is a false alarm detected.

In addition, in FIG. 15, at graph 1500, the line at 1504 representsprobability of a hole (or vacancy) being detected, the line at 1506represents probability that a hole is missed, and the line at 1508represents probability that there is a false alarm detected. Similarly,at graph 1502, the line at 1510 represents probability of a PU and SUdetected, the line at 1512 represents probability that a PU and SU aremissed, and the line at 1514 represents probability that there is afalse alarm detected. The proposed approach is shown to generate muchhigher probability of correctly identifying the PU and PU+SU, even atvery high array noise, though at a cost of very high false alarm.

Turning to FIG. 16, an exemplary non-limiting computing system oroperating environment in which various aspects described herein can beimplemented is illustrated. One of ordinary skill in the art canappreciate that handheld, portable and other computing devices andcomputing objects of all kinds are contemplated for use in connectionwith the claimed subject matter, e.g., anywhere that a communicationssystem may be desirably configured. Accordingly, the below generalpurpose remote computer described below is but one example of acomputing system in which the claimed subject matter can be implemented.

Although not required, the claimed subject matter can partly beimplemented via an operating system, for use by a developer of servicesfor a device or object, and/or included within application software thatoperates in connection with one or more components of the claimedsubject matter. Software may be described in the general context ofcomputer executable instructions, such as program modules, beingexecuted by one or more computers, such as client workstations, serversor other devices. Those skilled in the art will appreciate that theclaimed subject matter can also be practiced with other computer systemconfigurations and protocols.

FIG. 16 thus illustrates an example of a suitable computing systemenvironment 1600 in which the claimed subject matter can be implemented,although as made clear above, the computing system environment 1600 isonly one example of a suitable computing environment for a media deviceand is not intended to suggest any limitation as to the scope of use orfunctionality of the claimed subject matter. Further, the computingenvironment 1600 is not intended to suggest any dependency orrequirement relating to the claimed subject matter and any one orcombination of components illustrated in the example operatingenvironment 1600.

With reference to FIG. 16, an example of a remote device forimplementing various aspects described herein includes a general purposecomputing device in the form of a computer 1610. Components of computer1610 can include, but are not limited to, a processing unit 1620, asystem memory 1630, and a system bus 1621 that couples various systemcomponents including the system memory 1630 to the processing unit 1620.The system bus 1621 can be any of several types of bus structuresincluding a memory bus or memory controller, a peripheral bus, and alocal bus using any of a variety of bus architectures.

Computer 1610 can include a variety of computer readable media. Computerreadable media can be any available media that can be accessed bycomputer 1610. By way of example, and not limitation, computer readablemedia can comprise computer storage media and communication media.Computer storage media includes volatile and nonvolatile as well asremovable and non-removable media implemented in any method ortechnology for storage of information such as computer readableinstructions, data structures, program modules or other data. Computerstorage media includes, but is not limited to, RAM, ROM, EEPROM, flashmemory or other memory technology, CDROM, digital versatile disks (DVD)or other optical disk storage, magnetic cassettes, magnetic tape,magnetic disk storage or other magnetic storage devices, or any othermedium which can be used to store the desired information and which canbe accessed by computer 1610. Communication media can embody computerreadable instructions, data structures, program modules or other data ina modulated data signal such as a carrier wave or other transportmechanism and can include any suitable information delivery media.

The system memory 1630 can include computer storage media in the form ofvolatile and/or nonvolatile memory such as read only memory (ROM) and/orrandom access memory (RAM). A basic input/output system (BIOS),containing the basic routines that help to transfer information betweenelements within computer 1610, such as during start-up, can be stored inmemory 1630. Memory 1630 can also contain data and/or program modulesthat are immediately accessible to and/or presently being operated on byprocessing unit 1620. By way of non-limiting example, memory 1630 canalso include an operating system, application programs, other programmodules, and program data.

The computer 1610 can also include other removable/non-removable,volatile/nonvolatile computer storage media. For example, computer 1610can include a hard disk drive that reads from or writes tonon-removable, nonvolatile magnetic media, a magnetic disk drive thatreads from or writes to a removable, nonvolatile magnetic disk, and/oran optical disk drive that reads from or writes to a removable,nonvolatile optical disk, such as a CD-ROM or other optical media. Otherremovable/non-removable, volatile/nonvolatile computer storage mediathat can be used in the exemplary operating environment include, but arenot limited to, magnetic tape cassettes, flash memory cards, digitalversatile disks, digital video tape, solid state RAM, solid state ROMand the like. A hard disk drive can be connected to the system bus 1621through a non-removable memory interface such as an interface, and amagnetic disk drive or optical disk drive can be connected to the systembus 1621 by a removable memory interface, such as an interface.

A user can enter commands and information into the computer 1610 throughinput devices such as a keyboard or a pointing device such as a mouse,trackball, touch pad, and/or other pointing device. Other input devicescan include a microphone, joystick, game pad, satellite dish, scanner,or the like. These and/or other input devices can be connected to theprocessing unit 1620 through user input 1640 and associated interface(s)that are coupled to the system bus 1621, but can be connected by otherinterface and bus structures, such as a parallel port, game port or auniversal serial bus (USB). A graphics subsystem can also be connectedto the system bus 1621. In addition, a monitor or other type of displaydevice can be connected to the system bus 1621 via an interface, such asoutput interface 1650, which can in turn communicate with video memory.In addition to a monitor, computers can also include other peripheraloutput devices, such as speakers and/or a printer, which can also beconnected through output interface 1650.

The computer 1610 can operate in a networked or distributed environmentusing logical connections to one or more other remote computers, such asremote computer 1670, which can in turn have media capabilitiesdifferent from device 1610. The remote computer 1670 can be a personalcomputer, a server, a router, a network PC, a peer device or othercommon network node, and/or any other remote media consumption ortransmission device, and can include any or all of the elementsdescribed above relative to the computer 1610. The logical connectionsdepicted in FIG. 16 include a network 1671, such local area network(LAN) or a wide area network (WAN), but can also include othernetworks/buses. Such networking environments are commonplace in homes,offices, enterprise-wide computer networks, intranets and the Internet.

When used in a LAN networking environment, the computer 1610 isconnected to the LAN 1671 through a network interface or adapter 1660.When used in a WAN networking environment, the computer 1610 can includea communications component, such as a modem, or other means forestablishing communications over the WAN, such as the Internet. Acommunications component, such as a modem, which can be internal orexternal, can be connected to the system bus 1621 via the user inputinterface at input 1640 and/or other appropriate mechanism. In anetworked environment, program modules depicted relative to the computer1610, or portions thereof, can be stored in a remote memory storagedevice. It should be appreciated that the network connections shown anddescribed are exemplary and other means of establishing a communicationslink between the computers can be used.

Turning now to FIGS. 17-18, an overview of network environments in whichthe claimed subject matter can be implemented is illustrated. Theabove-described systems and methodologies can be applied to any wirelesscommunication network; however, the following description sets forthsome exemplary, non-limiting operating environments for said systems andmethodologies. The below-described operating environments should beconsidered non-exhaustive, and thus the below-described networkarchitectures are merely examples of network architectures into whichthe claimed subject matter can be incorporated. It is to be appreciatedthat the claimed subject matter can be incorporated into any nowexisting or future alternative communication network architectures aswell.

Referring first to FIG. 17, a wireless personal area network (WPAN)architecture 1700 based on the IEEE 802.15.3 high data rate WPANstandard is illustrated. Based on the IEEE 802.15.3 standard, the WPANarchitecture 1700 can include one or more piconets. As used herein, apiconet is an ad hoc network of independent data devices 1710-1728 thatcan engage in peer-to-peer communication. FIG. 17 illustrates one suchpiconet. In one example, the range of a piconet is confined to apersonal area of, for example, 10 to 50 meters, although a piconet canalternatively provide coverage for a larger or smaller coverage area.

In accordance with one aspect, a piconet can be established by a device1710 that is capable of becoming a piconet coordinator (PNC). The device1710 can establish the piconet by scanning a set of availablecommunication channels (e.g., communication channels corresponding totime frequency codes in an MB-OFDM communication environment) for achannel having a least amount of interference that is not in use byneighboring piconets. Once such a communication channel is found, thedevice 1710 can become a PNC and begin transmitting control messaging inthe form of beacons to allow other devices 1722-1728 to connect to thepiconet. As illustrated in architecture 1700, beacons transmitted by PNC1710 are shown by dotted lines.

Once a PNC 1710 establishes a piconet, one or more devices 1722-1728 canassociate with the PNC 1710 based on beacons transmitted by the PNC1710. In one example, beacons provided by a PNC 1710 can provide timinginformation, and a device 1722-1728 can perform one or more timingsynchronization techniques based on received beacons as described suprawhile associating with the piconet coordinated by the PNC 1710. Inaddition, beacons transmitted by the PNC 1710 can also containinformation relating to quality of service (QoS) parameters, time slotsfor transmission by devices 1722-1728 in the piconet, and/or othersuitable information. After a device 1722-1728 has successfullyassociated with the piconet, it can then communicate in the piconet bytransmitting data to the PNC 1710 and/or one or more other devices1722-1728 in the piconet. As illustrated in architecture 1700, datatransmissions are indicated by solid lines.

In accordance with one aspect, the PNC 1710 and devices 1722-1728 canadditionally communicate using ultra-wideband (UWB) communication. WhenUWB is used, the PNC 1710 and/or devices 1722-1728 can communicatebeacons and/or data using short-duration pulses that span a wide rangeof frequencies. In one example, transmissions made pursuant to UWB canoccupy a spectrum of greater than 20% of a center frequency utilized bythe network or a bandwidth of at least 500 MHz. Accordingly, UWBtransmissions can be conducted using a very low power level (e.g.,approximately 0.2 mW), which can allow UWB transmission to be conductedin common bands with other forms of communication without introducingsignificant interference levels. Because UWB operates at a low powerlevel, it should be appreciated that UWB is typically confined to asmall coverage area (e.g., approximately 10 to 100 meters), which cancorrespond to the coverage area of an associated piconet. However, bytransmitting in short radio bursts that span a large frequency range,devices utilizing UWB can transmit significantly large amounts of datawithout requiring a large amount of transmit power. Further, because ofthe large bandwidth range and low transmit power used in UWBtransmission, signals transmitted utilizing UWB can carry throughobstacles that can reflect signals at lower bandwidth or higher power.

Turning now to FIG. 18, various aspects of the global system for mobilecommunication (GSM) are illustrated. GSM is one of the most widelyutilized wireless access systems in today's fast growing communicationssystems. GSM provides circuit-switched data services to subscribers,such as mobile telephone or computer users. General Packet Radio Service(“GPRS”), which is an extension to GSM technology, introduces packetswitching to GSM networks. GPRS uses a packet-based wirelesscommunication technology to transfer high and low speed data andsignaling in an efficient manner. GPRS optimizes the use of network andradio resources, thus enabling the cost effective and efficient use ofGSM network resources for packet mode applications.

As one of ordinary skill in the art can appreciate, the exemplaryGSM/GPRS environment and services described herein can also be extendedto 3G services, such as Universal Mobile Telephone System (“UMTS”),Frequency Division Duplexing (“FDD”) and Time Division Duplexing(“TDD”), High Speed Packet Data Access (“HSPDA”), cdma2000 1x EvolutionData Optimized (“EVDO”), Code Division Multiple Access-2000 (“cdma20003x”), Time Division Synchronous Code Division Multiple Access(“TD-SCDMA”), Wideband Code Division Multiple Access (“WCDMA”), EnhancedData GSM Environment (“EDGE”), International MobileTelecommunications-2000 (“IMT-2000”), Digital Enhanced CordlessTelecommunications (“DECT”), etc., as well as to other network servicesthat shall become available in time. In this regard, the timingsynchronization techniques described herein may be applied independentlyof the method of data transport, and does not depend on any particularnetwork architecture or underlying protocols.

FIG. 18 depicts an overall block diagram of an exemplary packet-basedmobile cellular network environment, such as a GPRS network, in whichthe claimed subject matter can be practiced. Such an environment caninclude a plurality of Base Station Subsystems (BSS) 1800 (only one isshown), each of which can comprise a Base Station Controller (BSC) 1802serving one or more Base Transceiver Stations (BTS) such as BTS 1804.BTS 1804 can serve as an access point where mobile subscriber devices1850 become connected to the wireless network. In establishing aconnection between a mobile subscriber device 1850 and a BTS 1804, oneor more timing synchronization techniques as described supra can beutilized.

In one example, packet traffic originating from mobile subscriber 1850is transported over the air interface to a BTS 1804, and from the BTS1804 to the BSC 1802. Base station subsystems, such as BSS 1870, are apart of internal frame relay network 1810 that can include Service GPRSSupport Nodes (“SGSN”) such as SGSN 1812 and 1814. Each SGSN is in turnconnected to an internal packet network 1820 through which a SGSN 1812,1814, etc., can route data packets to and from a plurality of gatewayGPRS support nodes (GGSN) 1822, 1824, 1826, etc. As illustrated, SGSN1814 and GGSNs 1822, 1824, and 1826 are part of internal packet network1820. Gateway GPRS serving nodes 1822, 1824 and 1826 can provide aninterface to external Internet Protocol (“IP”) networks such as PublicLand Mobile Network (“PLMN”) 1845, corporate intranets 1840, orFixed-End System (“FES”) or the public Internet 1830. As illustrated,subscriber corporate network 1840 can be connected to GGSN 1822 viafirewall 1832; and PLMN 1845 can be connected to GGSN 1824 via boardergateway router 1834. The Remote Authentication Dial-In User Service(“RADIUS”) server 1842 may also be used for caller authentication when auser of a mobile subscriber device 1850 calls corporate network 1840.

Generally, there can be four different cell sizes in a GSMnetwork—macro, micro, pico, and umbrella cells. The coverage area ofeach cell is different in different environments. Macro cells can beregarded as cells where the base station antenna is installed in a mastor a building above average roof top level. Micro cells are cells whoseantenna height is under average roof top level; they are typically usedin urban areas. Pico cells are small cells having a diameter is a fewdozen meters; they are mainly used indoors. On the other hand, umbrellacells are used to cover shadowed regions of smaller cells and fill ingaps in coverage between those cells.

The claimed subject matter has been described herein by way of examples.For the avoidance of doubt, the subject matter disclosed herein is notlimited by such examples. In addition, any aspect or design describedherein as “exemplary” is not necessarily to be construed as preferred oradvantageous over other aspects or designs, nor is it meant to precludeequivalent exemplary structures and techniques known to those ofordinary skill in the art. Furthermore, to the extent that the terms“includes,” “has,” “contains,” and other similar words are used ineither the detailed description or the claims, for the avoidance ofdoubt, such terms are intended to be inclusive in a manner similar tothe term “comprising” as an open transition word without precluding anyadditional or other elements.

Additionally, the disclosed subject matter can be implemented as asystem, method, apparatus, or article of manufacture using standardprogramming and/or engineering techniques to produce software, firmware,hardware, or any combination thereof to control a computer or processorbased device to implement aspects detailed herein. The terms “article ofmanufacture,” “computer program product” or similar terms, where usedherein, are intended to encompass a computer program accessible from anycomputer-readable device, carrier, or media. For example, computerreadable media can include but are not limited to magnetic storagedevices (e.g., hard disk, floppy disk, magnetic strips . . . ), opticaldisks (e.g., compact disk (CD), digital versatile disk (DVD) . . . ),smart cards, and flash memory devices (e.g., card, stick). Additionally,it is known that a carrier wave can be employed to carrycomputer-readable electronic data such as those used in transmitting andreceiving electronic mail or in accessing a network such as the Internetor a local area network (LAN).

The aforementioned systems have been described with respect tointeraction between several components. It can be appreciated that suchsystems and components can include those components or specifiedsub-components, some of the specified components or sub-components,and/or additional components, according to various permutations andcombinations of the foregoing. Sub-components can also be implemented ascomponents communicatively coupled to other components rather thanincluded within parent components, e.g., according to a hierarchicalarrangement. Additionally, it should be noted that one or morecomponents can be combined into a single component providing aggregatefunctionality or divided into several separate sub-components, and anyone or more middle layers, such as a management layer, can be providedto communicatively couple to such sub-components in order to provideintegrated functionality. Any components described herein can alsointeract with one or more other components not specifically describedherein but generally known by those of skill in the art.

1. A system, comprising: a signal receiving component configured tomeasure one or more signals from one or more antennas in a firstfrequency band; a cyclostationary beamforming component configured toextract one or more signals of interest received in the first frequencyband using an adaptive cross self-coherent restoral process based on acycle frequency related to a primary device; and a signal identificationcomponent configured to determine whether the one or more signals ofinterest relate to the primary device.
 2. The system of claim 1, whereinthe signal identification component is configured to determine that theone or more signals of interest relate to the primary device based atleast in part on detection of a spectrum mainlobe in the one or moresignals of interest.
 3. The system of claim 1, further comprising atransmitter component configured to communicate data with a secondarydevice based at least in part on signals with different cyclefrequencies than the one or more signals of interest.
 4. The system ofclaim 1, further comprising a cognition management component configuredto determine whether to utilize a portion of a second frequency band forsecondary communication based at least in part on whether the one ormore signals of interest are related to the primary device.
 5. Thesystem of claim 4, further comprising a control action componentconfigured to utilize the portion of the second frequency band based atleast in part on a determination by the cognition management component.6. The system of claim 1, further comprising an information receivingcomponent configured to receive data representative of a cooperativemeasurement of one or more portions of the first frequency bandunutilized by the primary device from a common receiver.
 7. The systemof claim 1, wherein the signal identification component is furtherconfigured to determine whether the one or more signals of interestrelate to a secondary device or is vacant.
 8. The system of claim 1,wherein the cycle frequency is one of a conjugate cycle frequency or anon-conjugate cycle frequency.
 9. The system of claim 1, wherein thefirst frequency band is reserved for communication between primarydevices.
 10. The system of claim 1, wherein the cyclostationarybeamforming component is further configured to determine the cyclefrequency based on at least one of a carrier frequency, a symbol rate,or a predetermined signal property.
 11. A method, comprising: receivinga measurement of a frequency band from an antenna array; extracting asignal of interest from the frequency band by utilizing adaptivecross-coherent restoral based at least in part on a cycle frequency of aprimary device or a cycle frequency of a secondary device; anddetermining whether the frequency band is occupied by the primary deviceor the secondary device based at least in part on the signal ofinterest.
 12. The method of claim 11, wherein the determining includesdetecting a spectrum mainlobe in the signal of interest related to thecycle frequency of the primary device.
 13. The method of claim 12,further comprising selecting a portion of the frequency band forcommunicating with one or more secondary devices based at least in parton the detecting the spectrum mainlobe.
 14. The method of claim 11,wherein the determining whether the frequency band is occupied by thesecondary device includes detecting a spectrum mainlobe in the signal ofinterest related to the cycle frequency of the secondary device inresponse to detecting a sidelobe in the signal of interest related tothe cycle frequency of the primary device.
 15. The method of claim 11,wherein the determining includes determining whether the frequency bandis vacant.
 16. The method of claim 11, further comprising transmitting asignal to one or more disparate devices while receiving the measurementof the frequency band from the antenna array.
 17. The method of claim11, further comprising: receiving cooperative information from adisparate device that specifies whether the frequency band is occupiedby the primary device, the secondary device, or is vacant; and selectinga portion of the frequency band for communicating with one or moresecondary devices based at least in part on the cooperative information.18. The method of claim 11, further comprising transmitting datarepresentative of a result of the determining to a disparate device tofacilitate cooperative distribution of the data.
 19. The method of claim11, further comprising detecting, in the signal of interest, a secondarysidelobe or absence of a secondary sidelobe related to the cyclefrequency of the secondary device.
 20. The method of claim 11, furthercomprising detecting, in the signal of interest, a primary sidelobe orabsence of a primary sidelobe related to the cycle frequency of theprimary device.
 21. The method of claim 11, further comprisingdetermining the cycle frequency based on at least one of a carrierfrequency, a symbol rate, or a predetermined signal property.
 22. Asystem, comprising: means for receiving a measurement of a frequencyband from an antenna array; means for determining a signal of interestfrom the frequency band based at least in part on applyingcyclostationary beamforming to the measurement including applying anadaptive cross self-coherent restoral algorithm; and means foridentifying whether the frequency band is occupied by a primary device,a secondary device, or is vacant based at least in part on the signal ofinterest.
 23. The system of claim 22, further comprising means forselecting a portion of the frequency band for communicating with one ormore secondary devices.
 24. The system of claim 23, wherein the meansfor selecting includes means for detecting, in the signal of interest, aspectrum mainlobe related to a cycle frequency of the primary device.25. A computer-readable medium having store thereon computer-executableinstructions that, in response to execution, cause a computing system toperform operations, comprising: receiving one or more signals over afrequency band that have been transmitted by a primary component or asecondary component; and analyzing a cycle frequency of the one or moresignals using adaptive cross self-coherent restoral; and determiningwhether the one or more signals are associated with the primarycomponent or the secondary component based on the analyzing.
 26. Thecomputer-readable medium of claim 25, the operations further comprisinganalyzing a modulated signal coupled with at least one of a sinewavecarrier, a pulse train, coding, a repeated spreading, a hoppingsequence, or a cyclic prefix.
 27. The computer-readable medium of claim26, wherein the analyzing the modulated signal includes processing themodulated signal as a second-order cyclostationary signal in response toan associated mean and autocorrelation defining a periodicity.
 28. Thecomputer-readable medium of claim 27, wherein the processing themodulated signal includes processing the modulated signal as thesecond-order cyclostationary signal including processing non-overlappingfrequency bands that are uncorrelated.
 29. The computer-readable mediumof claim 27, wherein the processing the modulate signal includesprocessing the modulated signal as the second-order cyclostationarysignal in response to the associated mean and autocorrelation defining aspectral redundancy that results in correlation between non-overlappingspectral components separated by signal cycles.
 30. Thecomputer-readable medium of claim 25, wherein the analyzing includesdetermining the cycle frequency based on at least one of a carrierfrequency, a symbol rate, or a predetermined signal property.